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Predictions of nucleation theory applied to Ehrenfest thermodynamic transitions

A modified nucleation theory is used to determine a critical nucleus size and a critical activation-energy barrier for second-order Ehrenfest thermodynamic transitions as functions of the degree of undercooling, the interfacial energy, the heat-capacity difference, the specific volume of the transformed phase, and the equilibrium transition temperature. The customary approximations of nucleation theory are avoided by expanding the Gibbs free energy in a Maclaurin series and applying analytical thermodynamic expressions to evaluate the expansion coefficients. Nonlinear correction terms for first-order-transition calculations are derived, and numerical results are presented graphically for water and polystyrene as examples of first-order and quasi-second-order transitions, respectively.

Barker, R. E., Jr.↗

Analysis and design of a second-order digital phase-locked loop

A specific second-order digital phase-locked loop (DPLL) was modeled as a first-order Markov chain with alternatives. From the matrix of transition probabilities of the Markov chain, the steady-state phase error of the DPLL was determined. In a similar manner the loop's response was calculated for a fading input. Additionally, a hardware DPLL was constructed and tested to provide a comparison to the results obtained from the Markov chain model. In all cases tested, good agreement was found between the theoretical predictions and the experimental data.

Blasche, P. R.↗

Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis

In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.

Merchant, G. J.↗

Phase lags in Cygnus X-1

Coronae of hot electrons are ubiquitous features in models of the inner regions of accreting black holes and nonmagnetic neutron stars. The scattering optical depth of these coronae inferred from observations is often tau approximately 3, so the energy spectrum of the disk in these regions is likely masked by the spectrum of upscattered photons in the corona and some of the disk properties are thus obscured. Observations of the dependence on not available with the energy spectrum. In our picture, the disk emission is modeled as a photon source injected into a Comptonizing corona; Comptonization may also occur in the disk, but for our purposes the disk emission is simply an input to the corona. We show that, contrary to some claims, the functional dependence of lag on Fourier frequency emerges intact from transit through the corona, modulo a multiplicative factor (which may in principle be negative, so that a phase lag can be changed to a phase lead), even if the properties of the corona vary with time. We also show that any frequency dependence of the lag due to variation in the corona itself is only second order in the amplitude of the variation, and cannot exceed the transit time approximately ms of the corona; thus, the lags of up to 0.1 s seen in several black hole candidates come from lags in the emission from the disk. Finally, we predict that plots of the time lag versus Fourier frequency in black hole candidates should have a 'shelf' of constant lag equal to the coronal lag (approximately 1 ms), with the constant being proportional to In (E(sub 2)/E(sub 1)) for the lag between energies E(sub 2) and E(sub 1). The lack of such a shelf in current observations of several galactic black hole candidates constraints the radii of the coronae to be R less than or approximately = 10(exp 8) tau cm.

Miller, M. Coleman↗

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗

Leading-edge receptivity for blunt-nose bodies

This research program investigates boundary-layer receptivity in the leading-edge region for bodies with blunt leading edges. Receptivity theory provides the link between the unsteady distrubance environment in the free stream and the initial amplitudes of the instability waves in the boundary layer. This is a critical problem which must be addressed in order to develop more accurate prediction methods for boundary-layer transition. The first phase of this project examines the effects of leading-edge bluntness and aerodynamic loading for low Mach number flows. In the second phase of the project, the investigation is extended to supersonic Mach numbers. Singular perturbation techniques are utilized to develop an asymptotic theory for high Reynolds numbers. In the first year, the asymptotic theory was developed for leading-edge receptivity in low Mach number flows. The case of a parabolic nose is considered. Substantial progress was made on the Navier-Sotkes computations. Analytical solutions for the steady and unsteady potential flow fields were incorporated into the code, greatly expanding the types of free-stream disturbances that can be considered while also significantly reducing the the computational requirements. The time-stepping algorithm was modified so that the potential flow perturbations induced by the unsteady pressure field are directly introduced throughout the computational domain, avoiding an artificial 'numerical diffusion' of these from the outer boundary. In addition, the start-up process was modified by introducing the transient Stokes wave solution into the downstream boundary conditions.

Kerschen, Edward J.↗

Stochastic particle acceleration in solar flares

It is proposed that particles during the second phase of solar flares are accelerated by stochastic resonant scattering off hydromagnetic waves and first order Fermi acceleration in shock waves generated in the impulsive phase of the flare. Solutions allow arbitrary power law momentum dependences of the momentum diffusion coefficient as well as the momentum diffusion coefficient as well as the momentum loss time. The acceleration time scale to a characteristic energy approximately 100 keV for protons can be as short as 5s. The resulting electron spectra show a characteristic double power law with a transition around 200 keV and are correlated to the proton spectra evaluated under equal boundary conditions, indicating that electrons and protons are accelerated by the same mechanism. The correlation between the different spectral indices in the electron double power law and between electron and proton spectra are governed by the ratio of first to second order acceleration and therefore allow a determination of the Alfven Mach number of the shock wave.

Droege, W.↗

Airspace Technology Demonstration 2 (ATD-2): Integrated Arrival/ Departure/Surface (IADS) System Demonstration Technology Transfer Document Summary (ReadMe) Version 2 - Phase 2 Fused IADS

Airspace Technology Demonstration 2 (ATD-2) is part of NASA's Airspace Technology Demonstrations (ATD) Project under its Airspace Operations and Safety Program (AOSP). ATD-2 is a multi-year research and development effort to improve the predictability and operational efficiency of the air traffic system in metroplex environments while maintaining or improving throughput by enhancing and integrating arrival, departure, and surface prediction, scheduling, and management systems. In order to ensure that the products of this knowledge and technology transfer are relevant and useful, NASA has created strong partnerships with the FAA and industry stakeholders. This summary document and accompanying artifacts satisfy the second of three research transition products (RTPs) defined in the IADS research transition team (RTT) plan. This transfer consists of NASA's ATD-2 Phase 1 Baseline IADS and Phase 2 Fused IADS system capabilities

Capps, Alan↗

Gibbs free-energy difference between the glass and crystalline phases of a Ni-Zr alloy

The heats of eutectic melting and devitrification, and the specific heats of the crystalline, glass, and liquid phases have been measured for a Ni24Zr76 alloy. The data are used to calculate the Gibbs free-energy difference, Delta G(AC), between the real glass and the crystal on an assumption that the liquid-glass transition is second order. The result shows that Delta G(AC) continuously increases as the temperature decreases in contrast to the ideal glass case where Delta G(AC) is assumed to be independent of temperature.

Ohsaka, K.↗

Modeling of transitional flows

An effort directed at developing improved transitional models was initiated. The focus of this work was concentrated on the critical assessment of a popular existing transitional model developed by McDonald and Fish in 1972. The objective of this effort was to identify the shortcomings of the McDonald-Fish model and to use the insights gained to suggest modifications or alterations of the basic model. In order to evaluate the transitional model, a compressible boundary layer code was required. Accordingly, a two-dimensional compressible boundary layer code was developed. The program was based on a three-point fully implicit finite difference algorithm where the equations were solved in an uncoupled manner with second order extrapolation used to evaluate the non-linear coefficients. Iteration was offered as an option if the extrapolation error could not be tolerated. The differencing scheme was arranged to be second order in both spatial directions on an arbitrarily stretched mesh. A variety of boundary condition options were implemented including specification of an external pressure gradient, specification of a wall temperature distribution, and specification of an external temperature distribution. Overall the results of the initial phase of this work indicate that the McDonald-Fish model does a poor job at predicting the details of the turbulent flow structure during the transition region.

Lund, Thomas S.↗

The Strategy for the Second Phase of Aerobraking Mars Global Surveyor

On February 19, 1999, the Mars Global Surveyor (MGS) spacecraft was able to propulsively establish its mapping orbit. This event followed the completion of the second phase of aerobraking for the MGS spacecraft on February 4, 1999. For the first time, a spacecraft at Mars had successfully employed aerobraking methods in order to reach its desired pre-launch mapping orbit. This was accomplished despite a damaged spacecraft solar array. The MGS spacecraft was launched on November 7, 1996, and after a ten month interplanetary transit was inserted into a highly elliptical capture orbit at Mars on September 12, 1997. Unlike other interplanetary missions, the MGS spacecraft was launched with a planned mission delta-V ((Delta)V) deficit of nearly 1250 m/s. To overcome this AV deficit, aerobraking techniques were employed. However, damage discovered to one of the spacecraft's two solar arrays after launch forced major revisions to the original aerobraking planning of the MGS mission. In order to avoid a complete structural failure of the array, peak dynamic pressure levels for the spacecraft were established at a major spacecraft health review in November 1997. These peak dynamic pressure levels were roughly one-third of the original mission design values. Incorporating the new dynamic pressure limitations into mission replanning efforts resulted in an 'extended' orbit insertion phase for the mission. This 'extended' orbit insertion phase was characterized by two distinct periods of aerobraking separated by an aerobraking hiatus that would last for several months in an intermediate orbit called the "Science Phasing Orbit" (SPO). This paper describes and focuses on the strategy for the second phase of aerobraking for the MGS mission called "Aerobraking Phase 2." This description will include the baseline aerobraking flight profile, the trajectory control methodology, as well as the key trajectory metrics that were monitored in order to successfully "guide' the spacecraft to its desired mapping orbit. Additionally, the actual aerobraking progress is contrasted to the planned aerobraking flight profile. (A separate paper will describe the navigation aspects of MGS aerobraking in detail.) Key to the success of the MGS mission is the delivery of the spacecraft to its final mapping orbit and the synergy the instrument complement provides to its scientific investigators when science data is returned from that orbit. The MGS mapping orbit is characterized as a low altitude, near-circular, near-polar orbit that is Sun-synchronous with the descending equatorial crossing at 2:00 AM local mean solar time (LMST).

Johnston, M. D.↗

The phase diagram and transport properties for hydrogen-helium fluid planets

The properties of pure hydrogen and helium are examined, taking into account metallic hydrogen, molecular hydrogen, and the molecular-metallic transition. Metallic hydrogen-helium mixtures are considered along with molecular hydrogen-helium mixtures, the total phase diagram, and minor constituents, including deuterium. The transport properties of the metallic and the molecular phase are also discussed, giving attention to electrical conductivity, thermal conductivity, viscosity, self-diffusion, interdiffusion, radiative opacity, and second-order transport coefficients.

Stevenson, D. J.↗

Dilution Jet Mixing Program, phase 1

The effect of jet to mainstream density ratio, flow area convergence as encounted in transition sections, and nonuniform mainstream profile upstream of dilution orifices on the mixing of a row of jets with a confined cross flow was quantified. It is found that: (1) jet spreading rate in transverse direction is increased with increasing J, H/D and with decreasing S/D; (2) the density ratio has only a second order effect on the jet mixing characteristics for a constant momentum ratio; (3) the temperature distributions in the jet mixing region are strongly influenced by the undisturbed mainstream profile; (4) flow area convergence enhances mixing in radial and transverse directions. An asymmetric convergent duct with flat wall injection has the same jet mixing characteristics as a symmetric convergent duct. An asymmetric convergent duct with slant wall injection has a faster jet spreading rate in the transverse direction.

Srinivasan, R.↗

Adaptive Optimization for System Performance and Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

The emerging urban air mobility (UAM) sector in aerospace is driving development of unconventional multi-modal vehicle configurations and autonomous flight. The combination of multi-modal vehicle dynamics, complex environment, requirements to deal with flight contingencies in an efficient and safe manner, as well as necessity for precise trajectory following and performance, are the driving influence behind adaptive optimization for system performance. We are interested in trajectory optimization algorithm that would system parameter estimation and identifying the optimal switching time between modes of hybrid dynamical systems. This presentation discusses a parameterized optimal control trajectory optimization algorithm that is an extended and generalized version of Differential Dynamic Programming (DDP), titled Parameterized Differential Dynamic Programming (PDDP). DDP is an efficient trajectory optimization algorithm relying on second order approximations of a system’s dynamics and cost function and has recently been applied to optimize systems with time invariant parameters. Experiments are presented applying PDDP to solve model predictive control (MPC) and moving horizon estimation (MHE) tasks simultaneously. In particular, PDDP is used to determine the optimal transition point between flight regimes of a complex urban air mobility (UAM) class vehicle exhibiting multiple phases of flight and to identify and compensate for actuation faults.

optimization↗

Flare Statistics for Young Stars from a Convolutional Neural Network Analysis of TESS Data

All-sky photometric time-series missions have allowed for the monitoring of thousands of young (t(age) < 800 Myr) stars in order to understand the evolution of stellar activity. Here, we developed a convolutional neural network (CNN), stella, specifically trained to find flares in Transiting Exoplanet Survey Satellite (TESS) short-cadence data. We applied the network to 3200 young stars in order to evaluate flare rates as a function of age and spectral type. The CNN takes a few seconds to identify flares on a single light curve. We also measured rotation periods for 1500 of our targets and find that flares of all amplitudes are present across all spot phases, suggesting high spot coverage across the entire surface. Additionally, flare rates and amplitudes decrease for stars t(age) > 50 Myr across all temperatures T(eff) ≥ 4000 K, while stars from 2300 ≤ T(eff) < 4000 K show no evolution across 800 Myr. Stars of T(eff) ≤ 4000 K also show higher flare rates and amplitudes across all ages. We investigate the effects of high flare rates on photoevaporative atmospheric mass loss for young planets. In the presence of flares, planets lose 4%–7% more atmosphere over the first 1 Gyr. stella is an open-source Python toolkit hosted on GitHub and PyPI.

Adina D. Feinstein↗

A second-order all-digital phase-locked loop

A simple second-order digital phase-locked loop has been designed to synchronize itself to a square-wave subcarrier. Analysis and experimental performance are given for both acquisition behavior and steady-state phase error performance. In addition, the damping factor and the noise bandwidth are derived analytically. Although all the data are given for the square-wave subcarrier case, the results are applicable to arbitrary subcarriers that are odd symmetric about their transition region.

Holmes, J. K.↗

The long-term intensity behavior of Centaurus X-3

In three years of observation, the X-ray source Cen X-3 appears to alternate between 'high states', with an intensity of 150 counts/s (2-6 keV) or greater, and 'low states', where the source is barely detectable. The time scale of this behavior is of the order of months, and no apparent periodicity has been observed. Analysis of two transitions between these states is reported. During two weeks in July 1972, the source increased from about 20 counts/s to 150 counts/s. The detailed nature of this turn-on is interpreted in terms of a model in which the supergiant's stellar wind decreases in density. A second transition, a turnoff in February 1973, is similarly analyzed and found to be consistent with a simple decrease in accretion rate. The presence of absorption dips during transitions at orbital phases 0.4-0.5 as well as at phase 0.75 is discussed. The data are consistent with a stellar-wind accretion model and with different kinds of extended lows caused by increased wind density masking the X-ray emission or by decreased wind density lowering the accretion rate.

Schreier, E. J.↗